Grandpa Was Feeling Generous


Grandpa was feeling generous, so he gave a total of $100 to his 
five grandchildren. Starting with the youngest, each got $2.00 more
than the next younger one. In other words, the youngest got one 
sum, the next got $2.00 more, and so on. 

How much did the youngest grandchild get? 
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Answer:
$16

Solution:
Here's what each child received:
Child 1 $x
Child 2 $x + 2
Child 3 $x + 2 + 2
Child 4 $x + 2 + 2 + 2
Child 5 $x + 2 + 2 + 2 + 2

So, x + (x + 2) + (x + 2 + 2) + (x + 2 + 2 + 2) + (x + 2 + 2 + 2 + 2) = 100
or, 5x + 20 = 100
Simplify, 5x = 80 and x = 16

Proof:
Child 1 $16
Child 2 $18
Child 3 $20
Child 4 $22
Child 5 $24

16 + 18 + 20 + 22 + 24 = 100